Output Matching Model Reduction for Discrete‐Time Singular Systems With High Index

ABSTRACT In this paper, a new model order reduction approach is presented for reducing large‐scale discrete‐time singular systems with higher index. Based on the regularity of the singular system, the singular system is decomposed into a non‐singular subsystem and a singular subsystem. For the non‐singular subsystem, the output matching methods are respectively provided in the time and the frequency domains, so that the outputs of the reduced subsystem match a certain number of the outputs of the original subsystem. For the singular subsystem, output matching methods in both the time and the frequency domains are also obtained. Among them, all the outputs of the reduced non‐singular subsystem obtained by the frequency‐domain output matching method can theoretically approximate the outputs of the original non‐singular subsystem, while the frequency‐domain output matching method of the singular subsystem not only enables all outputs to match the original singular subsystem but also ensures the nilpotency of the reduced singular subsystem. Finally, a numerical example is provided to verify the effectiveness of the methods proposed in this paper.